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503
Rademacher chaos IN SYMMETRIC SPACES
, 2000
"... In this paper we study properties of series with respect to orthogonal systems {ri(t)rj(t)}i̸=j and {ri(s)rj(t)} ∞ i,j=1 in symmetric spaces on interval and square, respectively. Necessary and sufficient conditions for the equivalence of these systems with the canonical base in l2 and also for the ..."
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Cited by 2 (2 self)
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for the complementability of the corresponding generated subspaces, usually called Rademacher chaos, are derived. The results obtained allow, in particular, to establish the unimprovability of the exponential integrability of functions from Rademacher chaos. Besides, it is shown that for spaces that are ”close ” to L
RADEMACHER CHAOS IN SYMMETRIC SPACES, II
, 2008
"... In this paper we study some properties of the orthonormal system {rirj}1≤i<j<∞ where rk(t) are Rademacher functions on [0,1], k = 1,2,... This system is usually called Rademacher chaos of order 2. It is shown that a specific ordering of the chaos leads to a basic sequence (possibly nonuncondi ..."
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In this paper we study some properties of the orthonormal system {rirj}1≤i<j<∞ where rk(t) are Rademacher functions on [0,1], k = 1,2,... This system is usually called Rademacher chaos of order 2. It is shown that a specific ordering of the chaos leads to a basic sequence (possibly non
Rademacher Chaos Complexities for Learning the Kernel Problem
"... In this paper we develop a novel generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning problem reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, which we refer to as Rade ..."
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In this paper we develop a novel generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning problem reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, which we refer
Rademacher Chaos: Tail Estimates vs Limit Theorems
"... We study Rademacher chaos indexed by a sparse set which has a fractional combinatorial dimension. We obtain tail estimates for nite sums and a normal limit theorem as the size tends to in nity. The tails for nite sums may be much larger that the tails of the limit. ..."
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Cited by 2 (0 self)
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We study Rademacher chaos indexed by a sparse set which has a fractional combinatorial dimension. We obtain tail estimates for nite sums and a normal limit theorem as the size tends to in nity. The tails for nite sums may be much larger that the tails of the limit.
Generalization Bounds for Learning the Kernel: Rademacher Chaos Complexity
"... One of the central issues in kernel methods [5] is the problem of kernel selection (learning). This problem has recently received considerable attention which can range from the width parameter selection of Gaussian kernels to obtaining an optimal linear combination from a set of finite candidate ke ..."
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generalization bound for kernel learning problem. First, we show that generalization analysis of kernel learning algorithms reduces to investigation of the suprema of homogeneous Rademacher chaos process of order two over candidate kernels, which we refer to it as Rademacher chaos complexity. Our novel approach
Rademacher chaos, random eulerian graphs and the sparse johnsonlindenstrauss transform. ArXiv eprints, arXiv:1011.2590
 Emmanuel J. Candès and Michael
, 2010
"... ar ..."
Generalization bounds for learning the kernel
 In Proc. of the 22 nd Annual Conference on Learning Theory
, 2009
"... In this paper we develop a novel probabilistic generalization bound for learning the kernel problem. First, we show that the generalization analysis of the regularized kernel learning system reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, ..."
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Cited by 23 (4 self)
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In this paper we develop a novel probabilistic generalization bound for learning the kernel problem. First, we show that the generalization analysis of the regularized kernel learning system reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels
The Rademacher complexity of linear transformation classes
 Proc. 19th Annual Conference on Learning Theory (COLT
, 2006
"... Abstract. Bounds are given for the empirical and expected Rademacher complexity of classes of linear transformations from a Hilbert space H to a nite dimensional space. The results imply generalization guarantees for graph regularization and multitask subspace learning. 1 ..."
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Cited by 11 (2 self)
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Abstract. Bounds are given for the empirical and expected Rademacher complexity of classes of linear transformations from a Hilbert space H to a nite dimensional space. The results imply generalization guarantees for graph regularization and multitask subspace learning. 1
Stein’s method and stochastic analysis of Rademacher functionals
, 2008
"... Abstract: We compute explicit bounds in the Gaussian approximation of functionals of infinite Rademacher sequences. Our tools involve Stein’s method, as well as the use of appropriate discrete Malliavin operators. Although our approach does not require the classical use of exchangeable pairs, we emp ..."
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Cited by 9 (7 self)
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employ a chaos expansion in order to construct an explicit exchangeable pair vector for any random variable which depends on a finite set of Rademacher variables. Among several examples, which include random variables which depend on infinitely many Rademacher variables, we provide three main
Results 1  10
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503